Summary

Understanding and shaping the health of populations requires both qualitative and quantitative scientific methods. Statistical concepts are used to structure and manage the uncertainty inherent in the scientific study of human life, behavior, and society. In this workshop, I’ll share some of my experiences as a biostatistician and digital health data scientist—all (well, let’s say 95%) using R.

• “A Statistical New World” (youtu.be/NrDmVdHUtVQ)

Agenda

1. Your Host
2. Biostatistics and Data Science Settings
3. Career Paths
4. Study Designs
5. Analysis Methods
6. Wrap Up

1. Your Host

Geography

• PH (Parañaque + NCR / Metro Manila) \(\rightarrow\) CA (San Diego \(\rightarrow\) LA Metro) \(\rightarrow\)
• NY (Ithaca) \(\rightarrow\) CA (SF Bay Area) \(\rightarrow\)
• NC (Triangle Area) \(\rightarrow\) CA (SF Bay Area)

Training

• Loyola High School (Los Angeles) \(\rightarrow\)
• Cornell (BA Neurobiology + Animal Behavior) \(\rightarrow\) Cornell (MPS Applied Statistics) \(\rightarrow\)
• UNC Chapel Hill (DrPH Biostatistics) \(\rightarrow\)
• Stanford (Postdoctoral Research Fellowship)

Career

• pharma + clinical trials \(\rightarrow\)
• public health \(\rightarrow\)
• behavior change \(\rightarrow\)
• health tech + digital health

2. Biostatistics and Data Science Settings

• 🏥📃 health systems + health policy + healthcare (e.g., Affordable Care Act / Obamacare)
• 💻📄 bioinformatics (e.g., drug databases, healthcare claims)
• 📊 surveys + demographics (e.g., U.S. Census, American Community Survey)
• 🚬 🚌 environmental/occupational health (e.g., tobacco exposure, public transportation, workplace discrimination)
• 👶 maternal and child health (e.g., breastfeeding practices, perinatal care)
• 🍌 nutrition (e.g., obesity, sugar consumption, dieting trends)
• ☣️ infectious diseases + outbreaks (e.g., coronavirus, Ebola, STD/STIs, HIV)
• 🛌 chronic conditions (e.g., cancer, migraines, pain, drug addiction, AIDS)
• 🏃 health behavior and education (e.g., physical activity, stress, sleep, sexual health)
• 📱⌚️ digital health (e.g., Fitbit, Apple Watch, Garmin)
• 🖥 imaging (e.g., radiology, neuroscience)
• 🔬 omics (e.g., genetics/genomics, proteomics)

3. Biostatistics Career Paths

Training

• certifications: quantitative courses + MOOCs, bootcamps
• degrees: BA, BS, BSPH \(\rightarrow\) MS, MPH \(\rightarrow\) PhD, DrPH

Roles

• biostatistician, health statistician, medical statistician
• epidemiologist
• data scientist, health data scientist
• survey statistician, demographer, health economist

Professional Areas

• government (e.g., NIH, FDA, CDC, Census Bureau, state health department)
• academia/universities, research centers, institutes, foundations (e.g., Bill and Melinda Gates, RWJ)
• policy think tanks (e.g., RAND, Pew)
• industry (e.g., pharma/biotech, healthcare IT, digital health)

4. Study Designs

Variables

• outcome \(Y\) (e.g., 🤒 COVID-19 infection)
• explanatory variables
  • independent variable \(X\)
  • covariates \(Z\) (e.g., age, sex, race/ethnicity)

Designs

• 💊 randomized controlled trial (RCT): clinical trials
  • \(X\) is randomized treatment/intervention (e.g., Pfizer vaccine, hydroxychloroquine, Remdesivir)
  • goal: characterize \(X \rightarrow Y\), use \(Z\) to help
• 📈 observational study: epidemiology
  • \(X\) is non-randomized exposure or risk factor (e.g., pre-existing chronic health condition)
  • goal: characterize \(X \rightarrow Y\) or \(X \leftrightarrow Y\), use \(Z\) to help
• 🔬🖥 bench sciences (imaging, omics)
  • \(X\) is biological correlate or biomarker (e.g., SNPs)
  • goal: characterize \(X, Z, Y\) relationships

5. Analysis Methods: Foundations

“Confusing P-values with Clinical Impact: The Significance Fallacy”

Statistical Hypothesis Testing

• scientific hypothesis: \(Y\) varies by \(X\) on average
• null hypothesis \(H_0: \mu_1 = \mu_0\)
  • \(\mu_1 = E(Y|X=1)\) vs. \(\mu_0 = E(Y|X=0)\)
• alternative hypothesis \(H_1: \mu_1 \ne \mu_0\) (or \(H_A\))
• sample of \(i = 1, \dots, n\) observations
• test statistic \(TS_n\) and p-value
• statistical significance level \(\alpha\) often 0.05
  • arbitrary/traditional; i.e., not necessarily scientific
  • probability of Type 1 error (false positive)
• power to discern true positive \(1 - \beta\)
  • \(\beta =\) probability of Type 2 error (false negative)

5. Analysis Methods: Cross-Sectional Analysis

• \(i = 1, \dots, n\) patients
• \(\textbf{Y} = (\{Y_i\}) = (Y_1, \dots, Y_n)\)
• \(\textbf{X} = (\{X_i\}) = (X_1, \dots, X_n)\)
• \(Y\) continuous
  • linear regression: \(Y = \beta_0 + \beta_1 X + \varepsilon\) where \(\varepsilon \sim N(0, 1)\)
• \(Y = 0, 1\) binary
  • logistic regression: \(\text{logit} \Pr(Y=1) = \beta_0 + \beta_1 X\)
• many \(X_1, \dots, X_p\): model or feature selection
  • machine learning: regularization and cross-validation
  • “estimate \(E(Y|X_1, \dots, X_p)\) as \(\hat{E}(Y|X_1, \dots, X_p)\)” becomes “predict \(Y \sim \{ X_1, \dots, X_p \}\) as \(\hat{Y}\)”
  • \(Y\) continuous: prediction called “regression”
  • \(Y\) binary: prediction called “classification”

5. Analysis Methods: Cross-Sectional Analysis

Simulated/Synthetic Example: 12-week RCT of average treatment effect of two drugs on COVID-19 infection

• scientific hypothesis: probability of COVID-19 infection varies by drug on average
• \(Y\) represents infection status
  • \(Y_i = 1\) if infected, \(Y_i = 0\) if not infected
• \(X\) represents drug; randomized treatment assignment
  • \(X_i = 1\) if Remdazavir, \(X_i = 0\) if Feknuzison
• \(n_1 =\) 500, \(n_0 =\) 500
  • \(\textbf{Y} = (Y_1, \dots, Y_{1000})\)
  • \(\textbf{X} = (X_1, \dots, X_{1000})\)

5. Analysis Methods: Cross-Sectional Analysis

tbl_perpid_fancy %>%
  dplyr::select(
    `Patient ID`,
    Arm,
    `Infection Status`
  ) %>%
  dplyr::mutate(
    `Patient ID` = `Patient ID` %>% as.character,
    Arm = Arm %>% as.character,
    `Infection Status` = `Infection Status` %>% as.character
  ) %>%
  head %>%
  dplyr::bind_rows(
    dplyr::tibble(
      `Patient ID` = "...",
      Arm = "...",
      `Infection Status` = "..."
    )
  ) %>% knitr::kable(align = "c")

5. Analysis Methods: Cross-Sectional Analysis

tbl_perpid_fancy %>%
  dplyr::select(
    `Patient ID`,
    Arm,
    `Infection Status`
  ) %>%
  dplyr::mutate(
    `Patient ID` = `Patient ID` %>% as.character,
    Arm = Arm %>% as.character,
    `Infection Status` = `Infection Status` %>% as.character
  ) %>%
  head %>%
  dplyr::bind_rows(
    dplyr::tibble(
      `Patient ID` = "...",
      Arm = "...",
      `Infection Status` = "..."
    )
  ) %>% knitr::kable(align = "c")

tbl_perpid_fancy %>% fancyTable(c("Infection Status", "Arm"))

5. Analysis Methods: Cross-Sectional Analysis

5. Analysis Methods: Cross-Sectional Analysis

tbl_perpid_fancy %>% fancyTable(c("Infection Status", "Arm"))

5. Analysis Methods: Cross-Sectional Analysis

tbl_perpid_fancy %>% fancyTable(c("Infection Status", "Arm"))

fisher.test(
  x = tbl_perpid_fancy$trt,
  y = tbl_perpid_fancy$infection
)

## 
##  Fisher's Exact Test for Count Data
## 
## data:  tbl_perpid_fancy$trt and tbl_perpid_fancy$infection
## p-value = 0.02107
## alternative hypothesis: true odds ratio is not equal to 1
## 95 percent confidence interval:
##  0.1965155 0.8923482
## sample estimates:
## odds ratio 
##  0.4311286

5. Analysis Methods: Cross-Sectional Analysis

logistic regression: \(\text{logit} \Pr(Y=1) = \beta_0 + \beta_1 X\)

• estimated baseline odds of infection (i.e., under Feknuzison): \(\hat{\beta}_0 =\) 0.057 (probability of infection: 0.054)
• estimated odds ratio (OR) of infection (i.e., of Remdazavir relative to Feknuzison): \(\hat{\beta}_1 =\) 0.431
  • OR 95% confidence interval: 0.208, 0.841

5. Analysis Methods: Cross-Sectional Analysis

logistic regression: \(\text{logit} \Pr(Y=1) = \beta_0 + \beta_1 X\)

• estimated baseline odds of infection (i.e., under Feknuzison): \(\hat{\beta}_0 =\) 0.057 (probability of infection: 0.054)
• estimated odds ratio (OR) of infection (i.e., of Remdazavir relative to Feknuzison): \(\hat{\beta}_1 =\) 0.431
  • OR 95% confidence interval: 0.208, 0.841

## 
## Call:
## glm(formula = infection ~ trt, family = binomial, data = .)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -0.3332  -0.3332  -0.2204  -0.2204   2.7312  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)  -2.8633     0.1979 -14.471   <2e-16 ***
## trt          -0.8422     0.3529  -2.386    0.017 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 329.51  on 999  degrees of freedom
## Residual deviance: 323.35  on 998  degrees of freedom
## AIC: 327.35
## 
## Number of Fisher Scoring iterations: 6

5. Analysis Methods: Survival/Time-to-Event (TTE) Analysis

• \(T_i =\) time to infection (i.e., week of infection)
• \(C_i = 1\) if \(T_i\) observed, \(C_i = 0\) if \(T_i\) censored
• \(\textbf{Y}_i = (T_i, C_i)\)
• \(\textbf{Y} = (\textbf{Y}_1, \dots, \textbf{Y}_n) = \big( (T_1, C_1), \dots, (T_n, C_n) \big)\)
  • e.g., \(\big( (9, 1), (\text{NA}, 0), \dots, (2, 1) \big)\)

5. Analysis Methods: Survival/Time-to-Event (TTE) Analysis

5. Analysis Methods: Survival/Time-to-Event (TTE) Analysis

5. Analysis Methods: Longitudinal/Panel Analysis

5. Analysis Methods: Longitudinal/Panel Analysis

5. Analysis Methods: Longitudinal/Panel Analysis

5. Analysis Methods: Longitudinal/Panel Analysis

5. Analysis Methods: Missing Data

5. Analysis Methods: Missing Data

5. Analysis Methods: Missing Data

5. Analysis Methods: Advanced

Survey Sampling

• finite population of size \(N\): \((y_1, \dots, y_N)\)
• sample of size \(n\): \((Y_1, \dots, Y_n) = (R_1 y_1, \dots, R_n y_N)\) where \(n \le N\)

Demographics

• life table, actuarial, population trends over time

Bayesian Statistics

• Bayes’ Theorem: \(p(B|A) = \frac{p(A|B)p(B)}{p(A)}\)
• \(p(\beta | \textbf{Y}, \textbf{X}) \propto p(\textbf{Y} | \textbf{X}, \beta) \pi(\beta)\)

Machine Learning

• \(Y \sim f(X)\)
• supervised learning: find \(\hat{Y}\) (implicitly: find \(\hat{E}(Y|X)\))
• unsupervised learning: cluster analysis

5. Analysis Methods: Advanced

Econometrics, Sociology, Psychometrics

• structural equation modeling
• time series

Genomics

• genome-wide association studies (GWAS)
• Manhattan plot (p-values showing possible strong gene associations)

5. Analysis Methods: Advanced: Causal Inference

Directed Acyclic Graph (DAG)

• \(X \rightarrow Y\) implies \(p(Y|X) \ne p(Y)\)
  • different potential outcomes \(Y(0) \ne Y(1)\), where \(Y(x)\) is potential outcome \(Y\) if \(X=x\) is randomly assigned

5. Analysis Methods: Advanced: Causal Inference

Directed Acyclic Graph (DAG)

• \(X \rightarrow Y\) implies \(p(Y|X) \ne p(Y)\)
  • different potential outcomes \(Y(0) \ne Y(1)\), where \(Y(x)\) is potential outcome \(Y\) if \(X=x\) is randomly assigned

RCT / Clinical Trial

DiagrammeR::grViz("
digraph causal {

  # Nodes
  node [shape = plaintext]
  X [label = 'Drug \n (X)']
  C [label = 'Sickness Level \n (C)']
  Y [label = 'COVID-19 Infection \n (Y)']

  # Edges
  edge [color = black, arrowhead = vee]
  rankdir = LR
  X -> Y
  C -> Y
  
}",
width = 800,
height = 270
)

5. Analysis Methods: Advanced: Causal Inference

Directed Acyclic Graph (DAG)

• \(X \rightarrow Y\) implies \(p(Y|X) \ne p(Y)\)
  • different potential outcomes \(Y(0) \ne Y(1)\), where \(Y(x)\) is potential outcome \(Y\) if \(X=x\) is randomly assigned

Observational Study / Real World Data

DiagrammeR::grViz("
digraph causal {

  # Nodes
  node [shape = plaintext]
  X [label = 'Drug \n (X)']
  C [label = 'Sickness Level \n (C)']
  Y [label = 'COVID-19 Infection \n (Y)']

  # Edges
  edge [color = black, arrowhead = vee]
  rankdir = LR
  X -> Y
  C -> X
  C -> Y
  
}",
width = 800,
height = 270
)

5. Analysis Methods: Advanced: Causal Inference

Directed Acyclic Graph (DAG)

• \(X \rightarrow Y\) implies \(p(Y|X) \ne p(Y)\)
  • different potential outcomes \(Y(0) \ne Y(1)\), where \(Y(x)\) is potential outcome \(Y\) if \(X=x\) is randomly assigned

Observational Study / Real World Data

• confounding
  • confounder \(C\) affects both \(X\) and \(Y\)
  • biases estimate of average treatment effect of \(X\) on \(Y\)

5. Analysis Methods: Advanced: Causal Inference

Directed Acyclic Graph (DAG)

• \(X \rightarrow Y\) implies \(p(Y|X) \ne p(Y)\)
  • different potential outcomes \(Y(0) \ne Y(1)\), where \(Y(x)\) is potential outcome \(Y\) if \(X=x\) is randomly assigned

Observational Study / Real World Data

• selection bias
  • \(A\) and \(M\) independent
  • only using USA data: conditioning on collider \(C = 1\)
  • creates bias: spurious correlation between \(A\) and \(M\)
  • false conclusion: “Asians are naturally good at math!”

5. Analysis Methods: Advanced: Causal Inference

https://tinyurl.com/phkfwbz5

5. Analysis Methods: Advanced: Causal Inference

https://tinyurl.com/4zvuat8

5. Analysis Methods: Advanced: N-of-1

Daza EJ, Wac K, Oppezzo M. Effects of Sleep Deprivation on Blood Glucose, Food Cravings, and Affect in a Non-Diabetic: An N-of-1 Randomized Pilot Study. Healthcare 2020 Mar (Vol. 8, No. 1, p. 6). Multidisciplinary Digital Publishing Institute.

5. Analysis Methods: Advanced: N-of-1

Daza EJ, Wac K, Oppezzo M. Effects of Sleep Deprivation on Blood Glucose, Food Cravings, and Affect in a Non-Diabetic: An N-of-1 Randomized Pilot Study. Healthcare 2020 Mar (Vol. 8, No. 1, p. 6). Multidisciplinary Digital Publishing Institute.

5. Analysis Methods: Advanced: N-of-1 Causal Inference

SBM + JSM 2021

• “MoTR + PSTn: Building a Causal Engine For Estimating the Within-Individual Average Treatment Effect Using Wearable Sensors”
• Google Drive folder: tinyurl.com/7uk62c8y

6. Wrap Up: References

• “A Statistical New World” (youtu.be/NrDmVdHUtVQ)
• Daza EJ. Confusing P-values with Clinical Impact: The Signifcance Fallacy (Signifcance does not imply importance | but you need it to judge quality). Towards Data Science, 1 May 2020. (tinyurl.com/2vx58xwh)
• Daza EJ. Coronavirus, Telemedicine, and Race: Simulated Real-World Evidence | Causal inference tutorial in R using synthetic data (Part 1). Towards Data Science, 15 Apr 2020. (tinyurl.com/phkfwbz5)
• Daza EJ. Your Coronavirus Telemedicine Health App Might Be Overrated: How to Tell | Causal inference tutorial in R using synthetic data (Part 2). Towards Data Science, 21 Apr 2020. (tinyurl.com/4zvuat8)
• Daza EJ, Wac K, Oppezzo M. Effects of Sleep Deprivation on Blood Glucose, Food Cravings, and Affect in a Non-Diabetic: An N-of-1 Randomized Pilot Study. Healthcare 2020 Mar (Vol. 8, No. 1, p. 6). Multidisciplinary Digital Publishing Institute. (mdpi.com/2227-9032/8/1/6)
• Goldstein ND, LeVasseur M, McClure LA. On the convergence of epidemiology, biostatistics, and data science. Harvard Data Science Review. 2020 Apr 30;2(2). (hdsr.mitpress.mit.edu/pub/twqhhlhr/release/2)

6. Wrap Up: Causal Inference Books

• Hernán MA, Robins JM (2020). Causal Inference: What If. Boca Raton: Chapman & Hall/CRC. hsph.harvard.edu/miguel-hernan/causal-inference-book
• Pearl J, Glymour M, Jewell NP. Causal inference in statistics: A primer. John Wiley & Sons; 2016 Mar 7. bayes.cs.ucla.edu/PRIMER/

6. Wrap Up: Acknowledgements and Financial Disclosures

I originally created these slides for the 2020 Pilipinx American Public Health Conference (PAPHC). I thank PAPHC for motivating this presentation, and providing coordination and technical support. This presentation is independent of my work for Evidation Health, where I am a full-time employee.

6. Wrap Up: About the Presenter

Dr. Daza is a data science statistician and digital health data scientist who develops causal inference methods for personal (n-of-1) digital health. He works at Evidation Health (evidation.com). “Significance of evidence is not evidence of significance.” (tinyurl.com/94dc9vn5)

• Websites: ericjdaza.com (CV/resume: ericjdaza.com/resume) | statsof1.org
• Twitter: @ericjdaza | @statsof1 | @fsbiostats
• LinkedIn: @ericjdaza
• GitHub of slides
  • R markdown code: north-2021-daza.Rmd (gist.github.com/ericjdaza/81866c8e59d6d25159104b608d055aff)
  • R code: north-2021-daza.R (gist.github.com/ericjdaza/0715238fb39273dfa678dc5fbdab760d)

🤓😎🇵🇭

Thank you! Maraming Salamat!

😃😄🙏

Questions?